I'm trying to find lecture notes of Mahowald and Unell, titled "Lectures on Bott periodicity in stable and unstable homotopy at the prime 2". Does anyone happen to know if a copy exists online (and if it does, where I can find it)?

It is cited in Peter May's "Applications and generalizations of the approximation theorem", and in Mahowald's "Some homotopy classes generated by $\eta_j$". Both sources cite specific sections from the document, and in the latter reference, it is said to have been submitted to Springer Lecture Notes Series. Charles Rezk pointed out to me that it's also referenced in footnote 1 of Kuhn's "Geometry of James-Hopf maps", where it's said that the document dates from 1977.

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    $\begingroup$ Mark Mahowald has gone to the great homotopy group in the sky. But his co-author, who got his PhD under Mahowald at Northwestern in 1979, Alan David Unell genealogy.math.ndsu.nodak.edu/id.php?id=6875 , is apparently still with us. Maybe you can track him down. $\endgroup$ Jun 15, 2019 at 21:05
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    $\begingroup$ I don't have a copy of these notes. I am pretty sure that the reference to these in my 1982 Pacific J. paper (part of my thesis) was because I had showed that the EHP sequence was compatible with the filtration on QRP^infty coming from filtering projective space by its skeleta, and Mark and Alan had some version of this (maybe with a proof?) in their notes, and this was shown to me. $\endgroup$ Jun 19, 2019 at 15:12

3 Answers 3


I scanned the notes (apologies for the delay). Thanks a lot to Peter May for lending me the notes and for letting me scan them! Here's the link: http://www.mit.edu/~sanathd/mahowald-unell-bott.pdf.

  • $\begingroup$ You're going to get an S.B, next Spring? With all the research you've done, the Institute should award you a Ph.D. at the same time. $\endgroup$ Dec 29, 2019 at 16:16

This is Alan. I'm glad you kept them. My last copy was sent to a student in Indiana years ago. I. glad to have an electronic version...Alan

  • $\begingroup$ Oh, and welcome to MathOverflow. Gerhard "Don't Worry About Blue Mud" Paseman, 2019.12.29. $\endgroup$ Dec 29, 2019 at 20:54
  • $\begingroup$ I never thought I'd see the situation depicted in this famous ad occur in real life. $\endgroup$ Jan 18, 2020 at 16:50
  • $\begingroup$ Thank you for creating the notes! $\endgroup$
    – skd
    Jan 31, 2020 at 16:05

Sanath, you will be happy to learn that I do have these notes. I'll give them to you to copy after you arrive in Chicago Monday.


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